| DataSet | GRT low | GRT high | Distance Threshold | Proximity Criterion | Deers | Observations |
|---|---|---|---|---|---|---|
| 1 | 0 | 36 | 10 | last | 35 | 149 |
| 2 | 0 | 36 | 10 | nearest | 35 | 147 |
| 3 | 0 | 200 | 15 | score | 36 | 207 |
Modelling Fecal Cortisol Metabolites
Dr. Nicolas Ferry - Bavarian National Forest Park / Daniel Schlichting - StabLab
31 Jan 2025
Model FCM levels - amongst other covariables - on spatial and temporal distance to hunting activities.
Expectations:
Contains information of 809 faecal samples, including
Deer location at the time of hunting event is approximated by linear interpolation.
To identify relevant Hunting Events respective to a given FCM Sample, we introduce three selection parameters:
Among the relevant hunting events, the most relevant one is defined by one of the three introduced proximity criteria:
A hunting event is considered relevant to a FCM sample, if
we define the Scoring function as following:
\[ S(d, t) \propto \begin{cases} \frac{1}{d^2} \cdot f_\textbf{t}(t), t \sim \mathcal{N}(\mu, \sigma^2) &|t \leq \mu \\ \frac{1}{d^2} \cdot f_\textbf{t}(t), t \sim \mathcal{Laplace}(\mu, b) &|t > \mu \end{cases} \] where: \[ \begin{align*} d & \text{: Distance } \\ t & \text{: Time Difference } \\ \mu & \text{: GRT target = 19 hours } \end{align*} \]
Scores relative to \(t\) and \(d\)
Effect of \(t\) on the Score
We suggest three different Datasets for Modelling
| DataSet | GRT low | GRT high | Distance Threshold | Proximity Criterion | Deers | Observations |
|---|---|---|---|---|---|---|
| 1 | 0 | 36 | 10 | last | 35 | 149 |
| 2 | 0 | 36 | 10 | nearest | 35 | 147 |
| 3 | 0 | 200 | 15 | score | 36 | 207 |
For Modelling, we consider the following covariates, defined for each pair of FCM sample and most relevant hunting event:
We chose two different approaches to Modelling:
Family: Gamma
Log link for interpretability.
Let \(i = 1,\dots,N\) be the indices of deer and \(j = 1,\dots,n_i\) be the indices of FCM measurements for each deer.
\[ \begin{eqnarray} \textup{FCM}_{ij} &\sim& \mathcal{Ga}\left( \nu, \frac{\nu}{\mu_{ij}} \right) \\ \mu_{ij} &=& \mathbb{E}(\textup{FCM}_{ij}) = \exp(\eta_{ij}) \\ \eta_{ij} &=& \beta_0 + \beta_1 \textup{Pregnant}_{ij} + \beta_2 \textup{NumberOtherHunts}_{ij} + \\ && f_1(\textup{TimeDiff}_{ij}) + f_2(\textup{Distance}_{ij}) + \\ && f_3(\textup{SampleDelay}_{ij}) + f_4(\textup{DefecationDay}_{ij}) + \\ && \gamma_{i}, \\ \gamma_i &\sim& \mathcal{N}(0, \sigma_\gamma^2). \end{eqnarray} \]
Linear Effects:
| Dataset | Term | Estimate | Std. Error |
|---|---|---|---|
| Closest in Time | (Intercept) | 5.8243844 | 0.0533979 |
| Closest in Time | NumOtherHunts | -0.1370438 | 0.0614158 |
| Nearest | (Intercept) | 5.8123504 | 0.0541316 |
| Nearest | NumOtherHunts | -0.1026115 | 0.0596574 |
| Highest Score | (Intercept) | 5.8882327 | 0.0812529 |
| Highest Score | NumOtherHunts | -0.0112701 | 0.0141569 |
Not many observations after datafusion left for robust modelling
Trade-off between spatial and temporal distance
Sample Delay seems to be significant
Modelling Outcomes don’t show much difference
Trade-off between Complexity and Explainability
How to minimize spatial and temporal distance at the same time?
How to use a bigger Part of the Data?
Effect of Hunting on Red Deer